1758

January–March

• January 1 – Swedish biologist Carl Linnaeus (Carl von Linné) publishes in Stockholm the first volume (Animalia) of the 10th edition of Systema Naturae, the starting point of modern zoological nomenclature, introducing binomial nomenclature for animals to his established system of Linnaean taxonomy. Among the first examples of his system of identifying an organism by genus and then species, Linnaeus identifies the lamprey with the name Petromyzon marinus. He introduces the term Homo sapiens. (Date of January 1 assigned retrospectively.)
• January 20 – At Cap-Haïtien in Haiti, former slave turned rebel François Mackandal is executed by the French colonial government by being burned at the stake.
• January 22 – Russian troops under the command of William Fermor invade East Prussia and capture Königsberg with 34,000 soldiers; although the city is later abandoned by Russia after the Seven Years' War ends, the city again comes under Russian control in 1945 during World War II and is now named Kaliningrad.
• February 22 – A fleet of 158 British Royal Navy warships, under the command of Admiral Edward Boscawen, departs from Plymouth toward North America in an effort to conquer the French Canadian territories of New France. Many of the sailors die of nutritional deficiencies along the way, including the scurvy that kills 26 of the crew of HMS Pembroke, captained by future world explorer James Cook on his first long voyage.
• February 23 – Jonathan Edwards, the famed English theologian who had assumed the presidency of what is now Princeton University only a week earlier, sets an example for students and faculty by publicly receiving an inoculation against smallpox. Unfortunately, the vaccine contains live smallpox; Edwards develops the disease and dies on March 22 at the age of 54.
• March 16 – Members of the Comanche Nation loot and destroy the Spanish Mission Santa Cruz de San Sabá (near modern-day Menard, Texas) and kill eight of the people there, including the mission leader, Father Alonso Giraldo de Terreros.

April–June

• April 29 – Battle of Cuddalore: A British fleet under Sir George Pocock engages the French fleet of Anne Antoine, Comte d'Aché indecisively near Madras.
• May 21 – Seven Years' War – French and Indian War: Mary Campbell is abducted from her home in Pennsylvania by members of the Lenape Nation.
• June 8 – Seven Years' War – French and Indian War: Siege of Louisbourg: James Wolfe's attack at Louisbourg, Nova Scotia, commences.

• June 9–10 – Spanish-Barbary Wars – Battle of Cape Palos: a Spanish squadron of three ships of the line defeats a Barbary squadron made up of a ship of the line and a frigate.
• June 23 – Seven Years' War – Battle of Krefeld: Anglo-Hanoverian forces under Ferdinand of Brunswick defeat the French.
• June 30 – Seven Years' War – Battle of Domstadtl: Austrian forces under Ernst Gideon von Laudon and Joseph von Siskovits rout an enormous convoy with supplies for the Prussian army, guarded by strong troops of Hans Joachim von Zieten.

July–September

• July 6
  • Pope Clement XIII succeeds Pope Benedict XIV, as the 248th pope.
  • Seven Years' War – Battle of Bernetz Brook: British troops defeat the French.
• July 8 – Seven Years' War: French and Indian War: French forces hold Fort Carillon against the British at Ticonderoga, New York.
• July 25 – Seven Years' War – French and Indian War: The island battery at Fortress Louisbourg is silenced, and all French warships are destroyed or taken.
• August 3 – Seven Years' War – Battle of Negapatam: Off the coast of India, Admiral Pocock again engages d'Aché's French fleet, this time with more success.

• August 25 – Seven Years' War – Battle of Zorndorf: Frederick halts the Russian army of Count Wilhelm Fermor near the Oder.
• August 27 – Seven Years' War – British troops under the command of Colonel John Bradstreet capture Fort Frontenac (near the site of what is now Kingston, Ontario) from the French.
• September 3 – Távora affair: Joseph I of Portugal survives an assassination attempt.
• September 14 – Seven Years' War – French and Indian War: Battle of Fort Duquesne: A British attack on Fort Duquesne (modern-day Pittsburgh) is defeated.

October–December

• October 14 – Seven Years' War: Battle of Hochkirch: Frederick loses a hard-fought battle against the Austrians under Marshal Leopold von Daun, who besieges Dresden.
• November 25 – Seven Years' War: French and Indian War: French forces abandon Fort Duquesne to the British, who then name the area Pittsburgh.
• December 13 – The ship Duke William sinks in the North Atlantic, with the loss of over 360 lives, while deporting Acadians from Prince Edward Island to France.
• December 25 – Halley's Comet is sighted by Johann Georg Palitzsch, confirming Edmund Halley's 1705 prediction of its periodicity.

Date unknown

• The French build the first European settlement in what becomes Erie County, New York, at the mouth of Buffalo Creek.
• Rudjer Boscovich publishes his atomic theory, in Theoria philosophiae naturalis redacta ad unicam legem virium in nalura existentium.
• A fire destroys parts of Christiania, Norway.

• Marquis Gabriel de Lernay, a French officer captured during the Seven Years' War, establishes a military lodge in Berlin, with the help of Baron de Printzen, master of The Three Globes Lodge at Berlin, and Philipp Samuel Rosa, a disgraced former pastor.
• Okadaya (岡田屋), predecessor of AEON, a multiple retailer group, founded in Yokkaichi, Japan.^{[citation needed]}
• J. R. Geigy, predecessor of Novartis, a global pharmaceutical brand, founded in Basel, Switzerland.

Date unknown

• Georges Antoine Chabot, French jurist, statesman (d. 1819)
• Nicholas Fish, U.S. Revolutionary soldier (d. 1833)
• Anthimos Gazis, Greek scholar, philosopher (d. 1828)
• Samuel Hardy, U.S. lawyer and statesman from Virginia (d. 1785)
• Jamphel Gyatso, 8th Dalai Lama of Tibet (d. 1804)
• Charles Lee, U.S. Attorney General (d. 1815)
• Samuel Sterett, American politician, U.S. Representative for Maryland (d. 1833)
• Marie-Claire Heureuse Félicité, Empress of Haiti (d. 1858)

Probable

• Kamehameha I, King of Hawaii (d. c. 1819)

Date unknown

• François Mackandal, Haitian revolutionary leader, burned at the stake (b. c. 1730)
• Nathaniel Meserve, American shipwright (b. 1704)
• Hyder Ali and his Sepoy capture Bangalore from "Khande Rao of the Maratha Confederacy". (Part of the Seven Years' War).
• Verónica II Guterres, African monarch